Problem: Solve for $x$ and $y$ using elimination. ${-3x+2y = 11}$ ${4x-2y = -8}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $2y$ and $-2y$ cancel out. ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {-3x+2y = 11}\thinspace$ to find $y$ ${-3}{(3)}{ + 2y = 11}$ $-9+2y = 11$ $-9{+9} + 2y = 11{+9}$ $2y = 20$ $\dfrac{2y}{{2}} = \dfrac{20}{{2}}$ ${y = 10}$ You can also plug ${x = 3}$ into $\thinspace {4x-2y = -8}\thinspace$ and get the same answer for $y$ : ${4}{(3)}{ - 2y = -8}$ ${y = 10}$